1. Field of the Invention
The present invention generally relates to a GPS (Global Positioning System) method of and a GPS apparatus for measuring or positioning a current position of a movable body on the basis of radio waves received from GPS satellites and to a navigation system including the GPS apparatus. The present invention also relates to a program storage device and a computer data signal embodiment in a carrier wave, which allow a computer to function as the GPS apparatus.
2. Description of the Related Art
In recent years, a GPS measurement has been broadly used in a navigation system of a movable body such as a vehicle, an airplane, a ship, or the like. Coordinates of the GPS satellites, which are the basis of the GPS measurement, are obtained by solving the Kepler""s equation with the system time included in the transmitted data of the received radio waves i.e., in the down links, at a plurality of monitor stations on the earth. Then, an orbit constant (position) of the satellite as obtained in this manner is transmitted as one portion of the transmitted data of the transmitted radio wave i.e., the up link, to the corresponding GPS satellite. As a result, each GPS satellite transmits its own position information included in the down link data.
In the case of 3D (3-dimensional) positioning measurement based on the radio waves received from the GPS satellites in this kind, it measures a pseudo-range r, which is a distance from a GPS receiver to each GPS satellite, on the basis of (i) the position information of each GPS satellite included in the radio wave received from each GPS satellite and (ii) a time length required for the received radio wave coming from each GPS satellite to the GPS receiver, basically as to four GPS satellites. This pseudo-range r is represented as a four-variable function of a clock error t and the coordinates (x, y, z) of the GPS receiver. Therefore, if the four pseudo-ranges r are measured depending on the radio waves received from the four GPS satellites, the four functions are obtained, so that the clock error t and the coordinates (x, y, z) of the GPS receiver can be calculated by solving the four nonlinear simultaneous equations. Then, the above-calculated coordinates are regarded as the current position of a movable body on which the GPS receiver is mounted.
In fact, however, it often happens that the radio waves from five or more GPS satellites can be received at the same time, and thus, a positioning solution of five (or six or more) nonlinear simultaneous equations for four variables x, y, z and t are calculated by the least square method on the basis of the five or more pseudo-ranges r to increase a positioning accuracy.
By the way, one disadvantage of the GPS measurement is the generation of measurement error of the pseudo-range by a multi-path. More specifically, the radio wave from the GPS satellite may have other paths to go through to the GPS receiver after reflecting on the surface of a huge building or the like once or more times, in addition to the path to go direct to the GPS receiver, especially around the huge building such as a skyscraper, a high-rise building, or the like. This phenomenon, under which the radio waves are received at the same time through a plurality of radio wave paths from the one identical GPS satellite, is called as a xe2x80x9cmulti-pathxe2x80x9d. When the multi-path is generated, an error is generated in the time length required for the received radio waves coming to the GPS receiver, and on the basis of this error, an error is generated in the pseudo-range. Then, when the multi-path is generated, the pseudo-range based on a regular radio wave path and the pseudo-ranged based on an irregular radio wave path are irregularly and alternatively measured, so that the arrival time and the pseudo-range are changed or flickered at a short cycle. Thus, the accuracy of the GPS measurement deteriorates extremely.
Therefore, a device for detecting the generation of the multi-path is installed, and if the multi-path is generated, such a correction that the GPS satellite related to the generation of the multi-path is eliminated from an object of the GPS measurement is performed, for example. According to this detection and correction of the multi-path, when the generation of the multi-path is detected as for the one or more received radio waves, this or these are eliminated from the measurement object and it is performed the GPS measurement based on at least four received radio waves. Moreover, in the case that only three received radio waves are left as a result of eliminating the radio waves, in each of which the generation of the multi-path is detected ,from the measurement object because of a bad environment of receiving radio waves, such a technique that the GPS measurement is performed by switching the 3D positioning measurement to the 2D positioning measurement has been developed. More concretely, in the GPS 2D positioning measurement, the pseudo-range from each GPS satellite to the GPS receiver is measured by using (i) the time length required for the received radio wave to reach from each GPS satellite to the GPS receiver, and (ii) the position information of each GPS satellite, which is included in the radio wave received from each GPS satellite, basically about three GPS satellites under the assumption that their distances from the earth are rarely changed for a short time.
However, according to the present inventors"" research, the above-mentioned technique, which detects the generation of the multi-path and eliminates the error of the pseudo-range, is not essentially accurate on its detection. Thus, there is a problem that the radio wave received through the normal radio wave path may be often erroneously eliminated from the measurement object of the GPS measurement by misdetection of the multi-path and the accuracy of the GPS measurement further deteriorates.
It is therefore an object of the present invention to provide a GPS method and a GPS apparatus, which can detect the generation of the multi-path and correct an error of the pseudo-range caused by the effect of the multi-path, as well as reduce the deterioration of the positioning accuracy even when the generation of the multi-path is erroneously detected, a navigation system including the GPS apparatus, a program storage device and a computer data signal embodiment in a carrier wave, which allow a computer to function as the GPS apparatus.
The above object of the present invention can be achieved by a GPS method provided with: a measurement process of measuring each pseudo-range ri (i=1, 2, . . . , n) from respective one of received radio waves from n GPS satellites (n is a natural number equal to or greater than 3) captured by a GPS receiver mounted on a movable body; a detection process of detecting a generation of a multi-path of the respective one of the received radio waves; a first calculation process of approximately calculating a clock error t and coordinates (x, y, z) of the GPS receiver as a solution of n simultaneous equations by performing a convergence calculation with respect to n functions fi (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), each of the n functions fi (x, y, z, t) representing the pseudo-range ri; a second calculation process of approximately calculating the clock error t and the coordinates (x, y, z) as a solution of n+1 simultaneous equations by performing a convergence calculation with respect to total n+1 functions obtained by adding one xcex1 fn+1 (x, y, z, t) to the n functions fi (x, y, z, t), where the one xcex1 fn+1 (x, y, z, t) is obtained by applying a weighting xcex1 (xcex1 is a real number which is equal to or greater than 1) to one function fn+1 (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), the one function fn+1 (x, y, z, t) representing a pseudo-range rn+1 obtained when the center of the earth is regarded as one GPS satellite; an output process of outputting the coordinates (x, y, z) calculated in the first or second calculation process as current position data, which indicate a current position of the movable body; and a selection process of selecting the second calculation process when the generation of the multi-path is detected by the detection process.
According to the GPS method of the present invention, the measurement process measures each pseudo-range ri from the respective one of received radio waves from n GPS satellites captured by the GPS receiver. This measurement is basically performed by measuring a time length required for the arrival and by multiplying this by the velocity of light. Then, the detection process detects the generation of the multi-path on the received radio wave on the basis of whether or not the measurement result, which is supposed to be obtained experientially, experimentally, or theoretically when the multi-path is generated, is actually obtained; for example, such a result that the pseudo-range ri, as measured above, is unstable. Here, if the generation of the multi-path is not detected by the detection process, the first calculation process performs the convergence calculation, for example, that according to Newton method with respect to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri. Consequently, it approximately calculates the clock error t and the coordinates (x, y, z) as a positioning solution of the n nonlinear simultaneous equations. As a result, it calculates the coordinates (x, y, z), which indicate the current position of the movable body, with a high accuracy under the condition that the multi-path is not generated.
On the other hand, if the detection process detects the generation of the multi-path, the selection process selects the second calculation process. Then, the second calculation process performs the convergence calculation, for example, that according to Newton method with respect to the total n+1 functions obtained by adding one xcex1 fn+1 (x, y, z, t) to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri. This one xcex1 fn+1 (x, y, z, t) is obtained by applying a weighting xcex1 (xcex1 is a real number which is equal to or greater than 1) to one function fn+1 (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), which represents a pseudo-range rn+1 obtained when the center of the earth is regarded as one GPS satellite. Consequently, it approximately calculates the clock error t and the coordinates (x, y, z) as a positioning solution of the n+1 nonlinear simultaneous equations. As a result, under the condition of the multi-path generation, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the condition that the earth is regarded as the GPS satellite, the coordinates (x, y, z) as the positioning solution are stabilized. In the case that the generation of the multi-path is misdetected despite of non-generation of the multi-path in the detection process, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the condition that the earth is regarded as the GPS satellite, the coordinates (x, y, z) as the positioning solution are stabilized. Then, the output process outputs the coordinates, which have the decreased dispersion or deviation arose from an error caused by the multi-path generation or by the misdetection of it, as the current position data, which indicate the current position of the movable body.
As described above, both when the multi-path is actually generated and when the generation of the multi-path is misdetected, it is possible to calculate the coordinates (x, y, z) as the stable positioning solution without knowing which case is happening. Especially, considering such a reality that it is difficult to increase the accuracy in the detection of the multi-path generation, the present invention is extremely profitable in practice because it can obtain substantially the stable GPS measurement results despite of whether or not the detection of the multi-path generation is performed properly.
In one aspect of the GPS method, the n functions fi (x, y, z, t) are as follows: rixe2x80x2+(∂ri/∂x)xcex94x+(∂ri/∂y)xcex94y+(∂ri/∂z) xcex94z+(∂ri/∂t)xcex94t, where rixe2x80x2 is an approximate value of ri, the one function fn+1 (x, y, z, t) is as follows: rn+1xe2x80x2+(∂rn+1/∂x)xcex94x+(∂rn+1/∂y)xcex94y+(∂rn+1/∂z)xcex94z+(∂rn+1/∂t)xcex94t, where rn+1xe2x80x2 is an approximate value of rn+1, and the convergence calculation is a calculation for converging a pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| (i=1, 2, . . . , n) within a predetermined value in the n simultaneous equations in the first calculation process and a calculation for converging a pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| (i=1, 2, . . . , n, n+1) within a predetermined value in the n+1 simultaneous equations in the second calculation process.
According to this aspect, it is possible to calculate the coordinates (x, y, z) as the positioning solution by performing the calculation of converging the pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| within the predetermined value such as a very small value which is, for example, close to 0 relatively easily and quickly by using a computer or the like in the first and the second calculation processes.
The predetermined value used for this convergence calculation is set in correspondence to the desired positioning accuracy, and it generally approaches 0 with the positioning accuracy increased and generally departs from 0 with the positioning accuracy decreased. This kind of predetermined value is set in advance depending on the desired positioning accuracy experientially, experimentally, or theoretically.
In another aspect of the GPS method, the second calculation process uses a function fn+1 (x, y, z, t) which estimates the clock error t instead of the one function.
According to this aspect, if the detection process detects the generation of the multi-path, the second calculation process performs the convergence calculation, for example, that according to Newton method with respect to the total n+1 functions obtained by adding one function fn+1 (x, y, z, t) which estimates the clock error t to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri, after applying the weighting xcex1, which is equal to or greater than 1, to the one function fn+1 (x, y, z, t). Consequently, it approximately calculates the clock error t and the coordinates (x, y, z) as a positioning solution of the n+1 nonlinear simultaneous equations. As a result, under the condition of the multi-path generation, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the estimation of the clock error t, the coordinates (x, y, z) as the positioning solution are stabilized. In the case that the generation of the multi-path is misdetected despite of non-generation of the multi-path in the detection process, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the estimation of the clock error t, the coordinates (x, y, z) as the positioning solution are stabilized. Then, the output process outputs the coordinates, which have the decreased dispersion or deviation arose from an error caused by the multi-path generation or by the misdetection of it, as the current position data, which indicate the current position of the movable body.
As described above, both when the multi-path is actually generated and when the generation of the multi-path is misdetected, it is possible to calculate the coordinates (x, y, z) as the stable positioning solution without knowing which case is happening.
Incidentally, it is also possible to calculate the coordinates (x, y, z) as the positioning solution by solving n+2 nonlinear simultaneous equations using the one function which estimates the clock error in addition to the one function obtained under the condition that the center of the earth is regarded as one GPS satellite, after applying the weighting xcex1 to at least one of the functions.
In another aspect of the GPS method, the first calculation process calculates a positioning solution (x, y, z, t) in converging xcex94R=Axc2x7xcex94X within a predetermined value when a pseudo-range error matrix of (n, 1) type is xcex94R=(xcex94r1, xcex94r2, . . . , xcex94rn) and a position error matrix of (4, 1) type is xcex94X=(xcex94x, xcex94y, xcex94z, xcex94t) and a partial differential term matrix of (n, 4) type is A, and the second calculation process calculates a solution (x, y, z, t) in converging xcex94R=Axc2x7xcex94X within a predetermined value when a pseudo-range error matrix of (n+1, 1), in which the weighting xcex1 is applied to the n+1th row, is xcex94R=(xcex94r1, xcex94r2, . . . , xcex94rn, xcex1xc2x7xcex94rn+1) and a position error matrix of (4, 1) type is xcex94X=(xcex94x, xcex94y, xcex94z, xcex94t) and a partial differential term matrix of (n+1, 4) type in which the weighting xcex1 is applied to the n+1th row is A
According to this aspect, it is possible to calculate the coordinates (x, y, z) as the positioning solution by performing the calculation of converging xcex94R=Axc2x7xcex94X within the predetermined value such as a very small value which is, for example, close to 0 relatively easily and quickly by a matrix operation by using a computer or the like in the first and the second calculation processes.
In another aspect of the GPS method, the detection process detects the generation of the multi-path depending on whether or not the pseudo-range ri measured by the measurement process is unstable.
According to this aspect, the generation of the multi-path is detected by the detection process depending on whether or not the pseudo-range ri measured by the measurement process is unstable. In other words, if the pseudo-range ri is not unstable according to a predetermined standard, the detection process regards the multi-path as the one without the generation, and if the pseudo-range ri is unstable according to the predetermined standard, the detection process regards the multi-path as the one with the generation.
In this aspect, the detection process may be constructed to detect the generation of the multi-path on the basis of variance of the pseudo-range ri measured by the measurement process.
By constituting in this manner, it is possible to detect the generation of the multi-path with relatively high accuracy and ease on the basis of the fact that the variance or dispersion of measurement values often varies between the captured GPS satellites when the multi-path is generated.
Incidentally, the first and the second calculation process may be performed by, for example, solving n (or nxe2x88x921 or less) nonlinear simultaneous equations about the received radio waves remained after excluding one or more functions fi (x, y, z, t) corresponding to the received radio wave or waves, in each of which the multi-path generation is detected, from the operation object of the first and the second calculation processes. In general, the positioning solution can not be obtained if the operation object of the first and the second calculation processes are less than four functions including (i) the function which estimates the clock error and (ii) the function which indicates the pseudo-range and which is obtained when the center of the earth is regarded as the GPS satellite, so that at least four functions are adopted as the operation objects of the first and the second calculation processes.
The above object of the present invention can be achieved by a GPS apparatus comprising: a measurement device for measuring each pseudo-range ri (i=1, 2, . . . , n) from respective one of received radio waves from n GPS satellites (n is a natural number equal to or greater than 3) captured by a GPS receiver mounted on a movable body; a detection device for detecting a generation of a multi-path in the respective one of the received radio waves; a first calculation device for approximately calculating a clock error t and coordinates (x, y, z) of the GPS receiver as a solution of n simultaneous equations by performing a convergence calculation with respect to n functions fi (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), each of the n functions fi (x, y, z, t) representing the pseudo-range ri; a second calculation device for approximately calculating the clock error t and the coordinates (x, y, z) as a solution of n+1 simultaneous equations by performing a convergence calculation with respect to total n+1 functions obtained by adding one xcex1 fn+1 (x, y, z, t) to the n functions fi (x, y, z, t), where the one xcex1 fn+1 (x, y, z, t) is obtained by applying a weighting xcex1 (xcex1 is a real number which is equal to or greater than 1) to one function fn+1 (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), the one function fn+1 (x, y, z, t) representing a pseudo-range rn+1 obtained when the center of the earth is regarded as one GPS satellite; an output device for outputting the coordinates (x, y, z) calculated in the first or second calculation device as current position data, which indicate a current position of the movable body; and a selection device for selecting the second calculation device when the generation of the multi-path is detected by the detection device.
According to the GPS apparatus of the present invention, the measurement device measures each pseudo-range ri from the respective one of received radio waves from n GPS satellites captured by the GPS receiver. Here, if the generation of the multi-path is not detected by the detection device, the first calculation device performs the convergence calculation, for example, that according to Newton method with respect to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri. Consequently, it approximately calculates the clock error t and the coordinates (x, y, z) as a positioning solution of the n nonlinear simultaneous equations. As a result, it calculates the coordinates (x, y, z), which indicate the current position of the movable body, with a high accuracy under the condition that the multi-path is not generated.
On the other hand, if the detection device detects the generation of the multi-path, the selection device selects the second calculation process. Then, the second calculation device performs the convergence calculation, for example, that according to Newton method with respect to the total n+1 functions obtained by adding one xcex1 fn+1 (x, y, z, t) to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri. The one xcex1 fn+1 (x, y, z, t) is obtained by applying a weighting xcex1 (xcex1 is a real number which is equal to or greater than 1) to one function fn+1 (x, y, z, t) having such variables as the clock error t and the coordinates (x, y, z), which represents a pseudo-range rn+1 obtained when the center of the earth is regarded as one GPS satellite. As a result, under the condition of the multi-path generation, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the condition that the earth is regarded as the GPS satellite, the coordinates (x, y, z) as the positioning solution are stabilized. In the case that the generation of the multi-path is misdetected despite of non-generation of the multi-path in the detection device, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the condition that the earth is regarded as the GPS satellite, the coordinates (x, y, z) as the positioning solution are stabilized. Then, the output device outputs the coordinates, which have the decreased dispersion or deviation arose from an error caused by the multi-path generation or by the misdetection of it, as the current position data, which indicate the current position of the movable body.
As described above, both when the multi-path is actually generated and when the generation of the multi-path is misdetected, it is possible to calculate the coordinates (x, y, z) as the stable positioning solution without knowing which case is happening.
In one aspect of the GPS apparatus, the n functions fi (x, y, z, t) are as follows: rixe2x80x2+(∂ri/∂x)xcex94x+(∂ri/∂y)xcex94y+(∂ri/∂z) xcex94z+(∂ri /∂t) xcex94t, where rixe2x80x2 is an approximate value of ri, the one function fn+1 (x, y, z, t) is as follows: rn+1xe2x80x2+(∂rn+1/∂x)xcex94x+(∂rn+1/∂y)xcex94y+(∂rn+1/∂z)xcex94z+(∂rn+1/∂t)xcex94t, where rn+1xe2x80x2 is an approximate value of rn+1, and the convergence calculation is a calculation for converging a pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| (i=1, 2, . . . , n) within a predetermined value in the n simultaneous equations in the first calculation device and a calculation for converging a pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| (i=1, 2, . . . , n, n+1) within a predetermined value in the n+1 simultaneous equations in the second calculation device.
According to this aspect, it is possible to calculate the coordinates (x, y, z) as the positioning solution by performing the calculation of converging the pseudo-range error xcex94ri=|rixe2x88x92rixe2x80x2| within the predetermined value such as a very small value which is, for example, close to 0 relatively easily and quickly by using a computer or the like in the first and the second calculation devices.
In another aspect of the GPS apparatus, the second calculation device uses a function fn+1 (x, y, z, t) which estimates the clock error t instead of the one function.
According to this aspect, if the detection device detects the generation of the multi-path, the second calculation device performs the convergence calculation, for example, that according to Newton method with respect to the total n+1 functions obtained by adding one function fn+1 (x, y, z, t) which estimates the clock error t to the n functions fi (x, y, z, t), each of which represents the pseudo-range ri, after applying the weighting xcex1, which is equal to or greater than 1, to the one function fn+1 (x, y, z, t). As a result, under the condition of the multi-path generation, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the estimation of the clock error t, the coordinates (x, y, z) as the positioning solution are stabilized. In the case that the generation of the multi-path is misdetected despite of non-generation of the multi-path in the detection device, as the weighting xcex1 is applied to the terms associated with the pseudo-range rn+1 supposed to be stabilized in correspondence to the estimation of the clock error t, the coordinates (x, y, z) as the positioning solution are stabilized. Then, the output device outputs the coordinates, which have the decreased dispersion or deviation arose from an error caused by the multi-path generation or by the misdetection of it, as the current position data, which indicate the current position of the movable body.
In another aspect of the GPS apparatus, the first calculation device calculates a positioning solution (x, y, z, t) in converging xcex94R=Axc2x7xcex94X within a predetermined value when a pseudo-range error matrix of (n, 1) type is xcex94R=(xcex94r1, xcex94r2, . . . , xcex94rn), a position error matrix of (4, 1) type is xcex94X=(xcex94x, xcex94y, xcex94z, xcex94t), and a partial differential term matrix of (n, 4) type is A, and the second calculation device calculates a solution in converging xcex94R=Axc2x7xcex94X within a predetermined value when a pseudo-range error matrix of (n+1, 1) type in which the weighting xcex1 is applied to the n+1th row is xcex94R=(xcex94r1, xcex94r2, . . . , xcex94rn, xcex1xc2x7xcex94rn+1) and a position error matrix of (4, 1) type is xcex94X=(xcex94x, xcex94y, xcex94z, xcex94t) and a partial differential term matrix of (n+1, 4) type in which the weighting xcex1 is applied to the n+1th row is A.
According to this aspect, it is possible to calculate the coordinates (x, y, z) as the positioning solution by performing the calculation of converging xcex94R=Axc2x7xcex94X within the predetermined value such as a very small value which is, for example, close to 0 relatively easily and quickly by a matrix operation by using a computer or the like in the first and the second calculation devices.
In another aspect of the GPS apparatus, the detection device detects the generation of the multi-path depending on whether or not the pseudo-range ri measured by the measurement device is unstable.
According to this aspect, the generation of the multi-path is detected by the detection device depending on whether or not the pseudo-range ri measured by the measurement device is unstable. In other words, if the pseudo-range ri is not unstable according to a predetermined standard, the detection device regards the multi-path as the one without generation, and if the pseudo-range ri is unstable according to the predetermined standard, the detection device regards the multi-path as the one with generation.
In this aspect, the detection device detects the generation of the multi-path on the basis of a variance of the pseudo-range ri measured by the measurement device.
By constituting in this manner, it is possible to detect the generation of the multi-path with a relatively high accuracy and ease on the basis of the fact that the variance or dispersion of measurement values often varies between the captured GPS satellites when the multi-path is generated.
The above object of the present invention can be achieved by a navigation system provided with: the above-mentioned GPS apparatus of the present invention (including its various aspects); the GPS receiver; and a display device for displaying on map data the current position data outputted from the output device in a predetermined format.
According to the navigation system of the present invention, because it is provided with the above-mentioned GPS apparatus, even if the multi-path is not generated in practice, even if the generation of the multi-path is properly detected, and even if the generation of the multi-path is misdetected, it is possible to display the current position data on map data on the basis of the stable positioning results.
The above object of the present invention can be also achieved by a program storage device readable by a computer. The program storage device stores a program of instructions to cause the computer to function as at least one portion of the above-described GPS apparatus of the present invention (including its various aspects).
According to the program storage device, such as a CD-ROM (Compact Disc-Read Only Memory), a ROM, a DVD (DVD Read Only Memory), a floppy disk or the like, of the present invention, the above described GPS apparatus of the present invention can be relatively easily realized as a computer reads and executes the program of instructions or as it executes the program after downloading the program through communication device. Moreover, the program of instructions can be sent from a central device with an application program required for the navigation or other data such as a map.
The above object of the present invention can be also achieved by a computer data signal embodied in a carrier wave and representing a series of instructions for a computer. The series of instructions causes the computer to function as at least one portion of the above-described GPS apparatus of the present invention (including its various aspects).
According to the computer data signal embodied in the carrier wave of the present invention, as the computer downloads the program in the computer data signal through a computer network or the like, and executes this program, it is possible to realize the above described GPS apparatus of the present invention.